dcgain — Evaluate steady-state gain of SISO transfer-function models.

dcgain(sys) computes the low-frequency gain of an LTI model: the transfer-function value at s = 0 for continuous-time models or z = 1 for discrete-time models. RunMat currently implements the SISO tf subset.

Syntax

gain = dcgain(sys)

Inputs

Returns

Errors

How dcgain works

• Current RunMat support is limited to SISO tf objects; MATLAB also supports broader LTI model families and MIMO gain matrices.
• Returns a real scalar for real-valued gains and a complex scalar for complex-valued gains.
• Continuous-time models are evaluated at zero frequency.
• Discrete-time models are evaluated at z = 1.
• A typed integer array is not a valid sys input. Integer coefficients admitted by tf have already crossed the model constructor's numeric boundary and do not make dcgain an integer-array operation.
• The documented DC gain is infinite for systems with integrators. RunMat derives the sign or complex axis from the first nonzero local denominator coefficient at the DC evaluation point, avoiding spurious NaN components while preserving exact pole-zero cancellation as indeterminate.

GPU memory and residency

dcgain returns a host scalar for the currently supported SISO form. A resident numeric array is not a dynamic-system object and is rejected without gather or provider dispatch.

Examples

Continuous-time DC gain

H = tf(2, [1 3]);
dcgain(H)

Expected output:

ans = 0.6667

Infinite gain of an integrator

H = tf(2, [1 0]);
dcgain(H)

Expected output:

ans = Inf

How RunMat validates dcgain

dcgain validates the object boundary before provider access and evaluates SISO transfer-function numerator and denominator polynomials at the steady-state point. Tests cover finite gains, signed continuous integrator infinity, discrete integrator infinity, complex-axis singular direction, exact pole-zero cancellation, invalid integer sys inputs, and integer coefficients already admitted by tf; broader LTI families and MIMO gain matrices remain explicit general control-system gaps.

• Implementation: `crates/runmat-runtime/src/builtins/control/dcgain.rs`

See Correctness & Trust for the full methodology and coverage table.

Using dcgain with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how dcgain changes the result.

FAQ

Related Control functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how dcgain is executed, line by line, in Rust.

• View the source for dcgain in Rust on GitHub
• Learn how the RunMat runtime works
• Found a bug? Open an issue with a minimal reproduction.

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